捷联式航空重力测量算法比较

捷联式航空重力测量系统与平台式系统相比具有体积小、重量轻、功耗低等许多优点,近些年来取得了显著的研究进展.本文给出了捷联式航空重力测量的两种算法模型:捷联式惯性标量重力测量(SISG)和旋转不变式标量重力测量(RISG)模型,并对其误差模型作了初步讨论.利用我国首套捷联式航空重力仪SGA-WZ01在某海域的部分试验数据,对两种算法模型进行了比较分析,表明其差值之标准差对于200s的滤波长度小于0.5mGal.同时,利用两组重复测线数据估算了不同滤波尺度下的两种算法的内符合精度,表明SISG算法略优于RISG算法.对于200s和300s的滤波长度,SISG的内符合精度分别为1.06mGal和0.80mGal.     

The Gravity Module Assembly used in airborne full tensor gradiometry surveys

In airborne gravity gradiometry, the Gravity Module Assembly is an optional gravimeter unit that is mounted on the same stabilized platform as the Full Tensor Gradiometer. Direct measurements of the gravity field are needed from this device to constrain the long wavelengths when gradient data are integrated mathematically to form high-resolution gravity fields. The Gravity Module Assembly is, however, capable of providing independent gravity data with a specification approaching that expected from a dedicated airborne gravity system. Presented here is an error analysis of data from this instrument collected alongside the Full Tensor Gradiometer during an airborne survey. By having both gradiometry and gravity datasets, comparisons of the information content in these two types of measurement are made.     

The first airborne scalar gravimetry system based on SINS/DGPS in China

China has developed an airborne gravimetry system based on SINS/DGPS named SGA-WZ,the first system in which a strapdown inertial navigation system(SINS)has been used for airborne gravimetry in China.This gravity measurement system consists of a strap-down inertial navigation system and a differential global positioning system(DGPS).In April 2010,a flight test was carried out in Shandong Province of China to test the accuracy of this system.The test was designed to assess the repeatability and accuracy of the system.Two repeated flights and six grid flights were made.The flying altitude was about 400 m.The average flying speed was about 60 m/s,which corresponds to a spatial resolution of 4.8 km when using 160-s cutoff low-pass filter.This paper describes the data processing of the system.The evaluation of the internal precision is based on repeated flights and differences in crossover points.Gravity results in this test from the repeated flight lines show that the repeatability of the repeat lines is 1.6 mGal with a spatial resolution of 4.8 km,and the internal precision of grid flight data is3.2 mGal with a spatial resolution of 4.8 km.There are some systematic errors in the gravity results,which can be modeled using trigonometric function.After the systematic errors are compensated,the precision of grid flight data can be better than1 mGal.     

Gravity control network at airports in nigeria

A network of gravity of control bases located at most of the airports and airfields in Nigeria has been established as a means of controlling future gravimetric studies in Nigeriaand of integrating existing gravity surveys into a unified whole for the purpose of producing gravity anomaly maps for the country. The network will also provide a means of checking and adjusting gravimeter calibration differences to a common standard.The LaCoste and Romberg gravimeters, models G446, G464 and G468, used for the observations were transported between the base stations by means of a six-seater fixed-wing aircraft. The scale adopted of the network was the same as that of gravimeter G464 to which the other two meters were referenced. The absolute gravity values observed ranged from 978184.882 ± 0.014 mGal at Nguru to 977844.379 ± 0.020 mGal at Jos, yielding a gravity range of 340.503 mGal. The accuracy of the individual absolute gravity value is better than 0.030 mGal using a datum value of 978120.933 mGal for site 103401 estlished at the Kano International Airport. The 34 observation sites are illustrated with sufficient detail to permit reoccupation within 0.50 m to 1.0 m.     

Improving airborne strapdown vector gravimetry using stabilized horizontal components

Integrating the deflections of the vertical along the flight line can yield geoid profiles which are valuable in the study of geodesy and geophysics, fortunately, the deflections can be measured directly by vector gravimetry. Airborne vector gravimetry using a Strapdown Inertial Navigation System and the Global Navigation Satellite System (SINS/GNSS) has shown promising results in previous studies. However, the quality of the SINS and GNSS is a major limitation; in particular, the attitude errors induced by the gyros will result in large measurement errors to the horizontal components of the gravity disturbance, and these measurement errors represent the behavior of low-frequency trend. An airborne vector gravimetry method used to remove the bias and low-frequency trends in the gravity disturbance estimated for each survey line has been developed. This method uses the horizontal components of the gravity disturbance computed from EGM2008 (Earth Gravitational Model 2008) as a reference. Firstly, the horizontal measurement results obtained from the gravimeter are divided into high- and low-frequency components according to the resolution of the EGM2008, and then, the bias and low-frequency trends of the low-frequency components are corrected using a linear fit to the EGM2008 reference data. Finally, the ultimate results can be acquired after combining the high-frequency components and the corrected low-frequency components. The data used was obtained from the SGA-WZ, which is the first strapdown airborne gravimeter developed in China. The results of this method are promising. The internal accuracy of the gravity disturbance's horizontal components for repeated survey lines exceeds 3.5 mGal, and the corresponding resolution is approximately 4.8 km based on 160-s data smoothing and an airplane averaging speed of approximately 216 km/h. After applying the WCF (Wavenumber Correlation Filter), the internal accuracy of the horizontal components exceeds 2 mGal. This can satisfy the requirement of the application in geodesy and solid earth geophysics.     

航空重力测量的系统误差补偿

基于航空重力测量的基本数学模型,详细分析了航空重力测量的系统误差来源.大致可将系统误差分为三类,即停机坪重力基准值、比力初值的观测误差,格值、交叉耦合系数、摆杆尺度因子的标定误差和水平加速度改正的模型化误差等.然后,对每类系统误差的量级及其补偿方法进行了研究,指出水平加速度改正是引起系统误差的主要因素之一.大同、哈尔滨和渤海湾航空重力测量的实测数据分析均表明,在各项系统误差尤其是水平加速度改正得到有效补偿后,航空重力与地面(或船测)参考值的系统误差将小于1×10^-5m·s^-2.     

LaCoste&Romberg航空重力仪K因子的动态标定及其特性研究

摆杆尺度因子（K因子）是反映LaCoste&Romberg航空重力仪线性响应特性的最重要参数. 利用基于地面参考数据的外部标定法和基于交叉点不符值的内部标定法分别对其进行了标定，实测数据分析表明，K因子的内、外部标定结果非常一致，且利用新K因子计算的空中重力扰动，其精度较采用出厂值提高了02～04 mGal. 内部标定法具有较好的实际应用价值. 研究了K因子与滤波尺度的相关性，表明重力仪可能为一非线性响应系统，即K因子的大小与摆杆速度的变化有关.     

利用重复测线校正海空重力仪格值及试验验证

通过分析海空重力测量系统误差的形成机理,我们发现海空重力仪格值标定误差是引起系统性测量偏差的主要因素之一.本文简要介绍了重力仪格值的标定方法,分析论证了格值标定的精度要求,提出了利用东西正反向重复测线检测校正海空重力仪格值的计算模型和补偿方法,分析讨论了该方法的校正精度及其适用条件,利用航空重力实际观测网数据对该方法的合理性和有效性进行了数值验证,证明该方法对消除海空重力测量系统性偏差具有显著作用.     

Conforming Falcon‡ gravity and the global gravity anomaly

Gravity derived only from airborne gravity gradient measurements with a normal error distribution will have an error that increases with wavelength. It is straightforward in principle to use sparsely sampled regional gravimeter data to provide the long wavelength information, thereby conforming the derived gravity to the regional gravity. Regional surface or airborne gravimeter data are not always available and can be difficult and expensive to collect in many of the areas where an airborne gravity gradiometer survey is flown. However the recent release by the Danish National Space Centre of the DNSC08 global gravity anomaly data has provided regional gravity data for the entire earth of adequate quality for this purpose. Studies over three areas, including comparisons with ground, marine and airborne gravimetry, demonstrate the validity of this approach. Future improvements in global gravity anomaly data are expected, particularly as the product from the recently launched Gravity field and steady‐state Ocean Circulation Explorer (GOCE) satellite becomes available and these will lead directly to an improvement in the very wide bandwidth gravity available after conforming gravity derived from gravity gradiometry with the global gravity.     

航空重力测量中载体运动加速度的确定

航空重力测量是使用重力仪、GPS及其他传感器测定地球重力场的一种新型技术，其基本原理是利用重力仪测定包括重力加速度、载体运动加速度以及其他一些加速度在内的总加速度，从观测值中减去利用GPS确定的载体运动加速度，再加上一些改正，得到了重力加速度. 本文推导了确定载体运动加速度的直接解算法的公式，利用某次航空重力测量数据，分别在静态、动态两种情况下，分析了确定载体运动加速度精度. 结果表明：在静态、60s的平滑间隔条件下，载体加速度的确定精度是0.4—0.9mGal；在动态、90s的平滑间隔条件下，整个飞行测段载体运动加速度的确定精度是1—3mGal.     

Upward continuation of Dome-C airborne gravity and comparison with GOCE gradients at orbit altitude in east Antarctica

An airborne gravity campaign was carried out at the Dome-C survey area in East Antarctica between the 17th and 22nd of January 2013, in order to provide data for an experiment to validate GOCE satellite gravity gradients. After typical filtering for airborne gravity data, the cross-over error statistics for the few crossing points are 11.3 mGal root mean square (rms) error, corresponding to an rms line error of 8.0 mGal. This number is relatively large due to the rough flight conditions, short lines and field handling procedures used. Comparison of the airborne gravity data with GOCE RL4 spherical harmonic models confirmed the quality of the airborne data and that they contain more high-frequency signal than the global models. First, the airborne gravity data were upward continued to GOCE altitude to predict gravity gradients in the local North-East-Up reference frame. In this step, the least squares collocation using the ITGGRACE2010S field to degree and order 90 as reference field, which is subtracted from both the airborne gravity and GOCE gravity gradients, was applied. Then, the predicted gradients were rotated to the gradiometer reference frame using level 1 attitude quaternion data. The validation with the airborne gravity data was limited to the accurate gradient anomalies (T_XX, T_YY, T_ZZ and T_XZ) where the long-wavelength information of the GOCE gradients has been replaced with GOCO03s signal to avoid contamination with GOCE gradient errors at these wavelengths. The comparison shows standard deviations between the predicted and GOCE gradient anomalies T_XX, T_YY, T_ZZ and T_XZ of 9.9, 11.5, 11.6 and 10.4 mE, respectively. A more precise airborne gravity survey of the southern polar gap which is not observed by GOCE would thus provide gradient predictions at a better accuracy, complementing the GOCE coverage in this region.     

Error sources and data limitations for the prediction of surface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), which sometimes have to be predicted from surrounding observations. We use the Earth Gravitational Model 2008 (EGM2008) and the Australian National Gravity Database (ANGD) as examples of model and terrestrial observed data respectively to predict gravity at Australian National Levelling Network (ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BM gravity values and then into gravimetric height corrections (HCs). Our results indicate that an approximate ±1 arc-min horizontal position error of the BMs causes maximum errors in EGM2008 BM gravity of ~22 mGal (~55 mm in the HC at ~2200 m elevation) and ~18 mGal for ANGD BM gravity because the values are not computed at the true location of the BM. We use RTM (residual terrain modelling) techniques to show that ~50% of EGM2008 BM gravity error in a moderately mountainous region can be accounted for by signal omission. Non-representative sampling of ANGD gravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmert orthometric correction at ~2200 m elevation). For modelled gravity at BMs to be viable, levelling networks need horizontal BM positions accurate to a few metres, while RTM techniques can be used to reduce signal omission error. Unrepresentative gravity sampling in mountains can be remedied by denser and more representative re-surveys, and/or gravity can be forward modelled into regions of sparser gravity.     

Regional gravity field modeling based on rectangular harmonic analysis

Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy,and can provide fundamental information for geophysics,geodynamics,seismology,and mineral exploration.Rectangular harmonic analysis(RHA)is proposed for regional gravity field modeling in this paper.By solving the Laplace’s equation of gravitational potential in local Cartesian coordinate system,the rectangular harmonic expansions of disturbing potential,gravity anomaly,gravity disturbance,geoid undulation and deflection of the vertical are derived,and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients(RHC).We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations.In order to reduce the edge effects caused by periodic continuation in RHA,we propose the strategy of extending the size of computation domain.The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal.The accuracy of the 2.5′×2.5′geoid undulations computed from ground and airborne gravity data is 1 and 1.4cm,respectively.The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 mGal.Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model,which may be a new option for the representation of the fine structure of regional gravity field.     

Absolute airborne gravimetry: a feasibility study

We report here the results obtained during a feasibility study that was pursued in order to evaluate the performances of absolute airborne gravimetry. In contrast to relative systems, which use spring‐type gravimeters, each measurement acquired by absolute systems is independent from the others and the instrument is not suffering from problems like instrumental drift, frequency response of the spring and variation of the calibration factor. After a validation of the dynamic performance of the experimental setup in a moving truck, a comparison between the experimental airborne data retrieved over the Swiss Alps and those obtained by ground upward continuation at flight altitude allow us to state that airborne absolute gravimetry is feasible. The first test flight shows a spatial resolution comparable to those obtained by relative airborne gravimetry. For a wavelength on the order of 12 km the absolute value of gravity can be evaluated with an uncertainty of 6.9 mGal.     

基于泊松小波径向基函数融合多源数据的局部重力场建模

融合多源数据的高精度、高分辨率的局部重力场建模是物理大地测量学的前沿和热点问题.本文研究了基于径向基函数融合多源数据的局部重力场建模方法,利用Monte-Carlo方差分量估计实现了不同类型的观测数据的合理定权,引入了最小标准差法确定基函数的适宜网络,分析了地形因素对于基函数网络确定及局部重力场建模精度的影响.以泊松小波基函数为构造基函数,结合残差地形模型,融合实测的陆地重力异常、船载重力异常及航空重力扰动数据构建了局部区域陆海统一的似大地水准面模型.研究结果表明:引入残差地形模型平滑了地形质量引入的高频扰动信号,简化了基函数的网络设计;并提高了重力似大地水准面的精度,平原地区其精度提高了4mm,地形起伏较大的山区其精度提高了约5cm.总体而言,基于"三步法"构建的局部重力似大地水准面在荷兰、比利时及德国相关区域,其精度分别达到1.12cm、2.80cm以及2.92cm.     

Using ground gravity to improve ice mass change estimation from GOCE gravity gradients in mid-west Greenland

Vertical gravity gradient anomalies from the Gravity and steady-state Ocean Circulation Explorer (GOCE) DIR-3 model have been used to determine gravity anomalies in mid-west Greenland by using Least-Squares Collocation (LSC) and the Reduced Point Mass (RPM) method. The two methods give nearly identical results. However, compared to LSC, the RPM method needs less computational time as the number of equations to be solved in LSC equals the number of observations. The advantage of the LSC, however, is the acquired error estimates. The observation periods are winter 2009 and summer 2012. In order to enhance the accuracy of the calculated gravity anomalies, ground gravity data from West Greenland is used over locations where the gravity change resulting from ice mass changes is negligible, i.e. over solid rock. In the period considered, the gravity anomaly change due to changes in ice mass varies from ?5 mGal to 4 mGal. It is negative over the outlet glacier Jacobshavn Isbræ, where the mass loss corresponds to a gravity change of approximately ?4 mGal. When using only GOCE vertical gravity gradients, the error estimates range from 5 mGal at the coast to 17 mGal over the ice sheet. Introducing the ground gravity data from West Greenland in the prediction reduces the errors to range from 2 to 10 mGal.     

自适应卡尔曼滤波在航空重力异常解算的应用研究

依据航空重力测量基本原理,构建了航空重力异常解算的卡尔曼滤波模型,将新息自适应卡尔曼滤波器(IAE,Innovation based Adaptive Estimation)应用于量测噪声未知的航空重力异常解算.针对IAE滤波器滑动窗口宽度难以准确确定的问题,通过对多个不同滑动窗口新息协方差估计的加权平均,获得改进的IAE滤波器,该IAE滤波器不仅具有量测噪声自适应估计能力,还能实现滑动采样窗口的优化选取.试验结果表明,IAE滤波器可以降低因量测噪声统计信息不明引起的解算误差,改进IAE解算的重力异常误差约为1mGal.     

数字重力仪高精度恒温测温系统设计与测试研究

高精度数字重力仪广泛应用于矿产资源勘探领域,由石英弹性系统组成的重力传感器是高精度数字重力仪的核心部件,其对外界环境温度非常敏感,由环境温度变化引起的重力输出变化远远大于仪器本身精度指标,而且不同的数字重力仪具有不同的温度影响特性.若重力传感器的恒温环境得不到保障,或环境温度的微弱变化无法得到准确的测量和补偿,将严重影响重力仪器的测量精度和一致性.本文针对该问题,研究了高精度恒温测温系统的设计方法及关键技术,考虑到数字重力仪器精度高、体积小、功耗低和便携式的特点,对高精度恒温测温系统中的关键器件选型、热结构设计、电路设计、软件设计等进行深入研究,并给出具体的解决措施.并设计了静态试验、高低温试验和石英弹性系统温度系数测定试验三个部分验证高精度恒温测温系统的有效性.试验结果表明：高精度测温系统最小分辨率达到10 μ℃;静态常温时,高精度恒温系统温度变化约为70 μ℃;在-20℃~+45℃的环境温度冲击中高精度恒温系统温度变化小于1 m℃;恒温点微调装置可实现石英弹性系统温度系数的精确测定.该研究为高精度重力测量仪器研制中消除环境温度变化影响提供了一种有效解决方案.     

引入最优自适应因子的状态模型法航空重力测量

引入最优自适应比例因子以改善状态模型法航空重力测量的精度,并尝试将其应用到我国困难地区的重力测量.把重力扰动当作状态量引入Kalman滤波进行最优估计,并引入最优自适应因子调节状态信息的权阵,提高重力扰动的最终解算精度.利用新疆地区不同航次和航高的实测数据,计算了垂直向下方向上的重力扰动.与全球重力场模型EGM2008的对比分析表明,差值中误差在10mGal左右,接近国家在困难地区重力测量精度的限差要求.     

融合多源数据构建区域航空重力梯度扰动全张量

通过联合全球重力位模型(EGM2008)、航空重力扰动数据和剩余地形模型(RTM)数据,基于频谱域(二维FFT变换)和空间域(Stokes数值积分)算法对毛乌素测区GT-2A航空重力测量系统采集的空中测线后处理重力扰动数据进行解算,构建了该地区的航空重力梯度扰动全张量.(1)残余航空重力扰动延拓结果表明:残余航空重力扰动经向下延拓至大地水准面,再向上延拓至航空高度后与原数据差值的标准差为1.0078 mGal,考虑边缘效应后,内缩计算范围得到的差值标准差减小至0.1269 mGal.(2)基于残余重力扰动数据(原航空高度数据及向下延拓数据),通过不同方案解算得到的梯度扰动结果表明:两种方案得到的研究区域重力梯度扰动各分量之差的最大标准差为6.4798E(Γ_(yz)分量),最小标准差为2.6968E(Γ_(xy)分量),内缩计算范围后得到的差值标准差最大值为1.8307E(Γ_(zz)分量),最小值为0.7223E(Γ_(yz)分量).本文的思路和方法可为未来我国自主构建航空重力梯度标定场提供参考.